The Mechanism · Gated-generation receipt

gen-state-dijkstra-s-algorithm-precisely-and-explain-why-it-matt-259f

stable pending witness
2026-05-29 08:01:19 UTC · anthropic/claude-sonnet-4-5

Prompt

State Dijkstra's algorithm precisely and explain why it matters in 2-3 sentences.
81 chars

Generation

# Dijkstra's Algorithm **Precise Statement:** Given a weighted graph with non-negative edge weights and a source vertex s, initialize all distances as infinite except d(s) = 0. Repeatedly select the unvisited vertex u with minimum distance, mark it as visited, and for each unvisited neighbor v, update d(v) = min(d(v), d(u) + weight(u,v)) until all reachable vertices are visited. **Why It Matters:** Dijkstra's algorithm efficiently finds the shortest paths from a source to all other vertices in O((V + E) log V) time with a priority queue, making it fundamental for navigation systems, network routing protocols, and countless optimization problems. It's one of the most widely implemented algorithms in real-world software, powering everything from GPS directions to internet packet routing.
28 tokens in · 190 tokens out · 5536 ms · $0.0029

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
5545.7 ms
Base LLM
5536.1 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0029

Trail

08:01:19 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
08:01:19 red_gate decision=pass reason=no disqualifying input patterns detected
08:01:24 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=190 latency_ms=5536.1 cost_usd=0.0029
08:01:24 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:01:24 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:01:24 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:01:24 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:01:24 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:01:24 signed hash_algo=sha256 hash=sha256:69e03885e5cb01a4495c77181224a4878fb8d658e7010bb8e4c14d0c542a77ae

Content hash

sha256:69e03885e5cb01a4495c77181224a4878fb8d658e7010bb8e4c14d0c542a77ae

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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